Such crystals are used extensively in the radio communication industry. Exemplary uses include IF filter and discriminator applications in mobile and cellular radios. Coupled-dual resonator crystals are preferred in many applications because they provide the characteristics of a very narrow filter due to the extremely high Q of the associated crystal resonators, as well as the narrow coupling between resonators. Such very narrow filter characteristics are virtually impossible or extremely difficult to realize with lumped devices, such as inductors and capacitors.
At the time the original Peppiatt and Roberts methodology was invented, as taught in U.S. Pat. No. 4,093,914, coupled-dual resonator crystals were designed to operate at frequencies only as high as the low 20 megahertz ("MHz") range. Currently, units at 45 MHz and 57.5 MHz are routinely built in production. Because of the requirements for higher and higher IF frequencies for cellular and mobile radios, with units in the 70 MHz to 90 MHz frequency range being used or considered in new product applications, the requirement for superior measurement accuracy for such high frequency coupled-dual resonator crystals is vitally important for testing and fabricating coupled-dual crystals and for producing high frequency monolithic crystal filters which meet the new radio specifications.
Key characteristics of these coupled dual crystals must be measured during the fabrication process as well as at the final test operation. A need exists for a reliable, accurate, and repeatable process for determining these characteristics of a coupled-dual resonator crystal. In particular, four critical frequencies, F1, F2, F3, and F4 must be determined in order to calculate first and second resonator frequencies, the normalized center frequency, the synchronous peak separation frequency and resonator inductances.
U.S. Pat. No. 4,093,914 discloses a process for measuring the four critical frequencies in coupled-dual resonator crystals and the formulas for determining the resonator frequencies, the normalized center frequency, and the synchronous peak separation frequency. The Peppiatt and Roberts methods involve determining four critical frequencies by monitoring, in the first case (Case I), one of the two crystal ports while shorting the second port. In the second case (Case II), they are determined by monitoring one of the two crystal ports while shorting the second port to obtain two frequencies and effectively open circuiting the second port or connecting a capacitor across it to obtain the other two frequencies. In the third case (Case III, taught in U.S. Pat. No. 5,047,726, the four critical frequencies are obtained by first monitoring the first port with the second port effectively open circuited, or with a capacitor connected across the second port, to obtain two of the frequencies, and then by monitoring the second port with the first port short circuited to obtain the other two critical frequencies. In each of the three cases, each of the four critical frequencies corresponds to the zero phase crossing of the voltage phase response at or near the particular voltage amplitude maximum or minimum for the particular Case in question.
It was discovered in U.S. Pat. No. 5,049,828 that as the desired fundamental or overtone operating frequencies of such coupled-dual resonator crystals increase and/or the effective resonator resistances increase, the measured phase excursions below the zero phase reference diminish and eventually fail to cross the zero phase reference. Also, it was additionally discovered that where one of the resonator frequencies (FA, for example) is much lower than that of the other resonator frequency (FB), the voltage amplitudes associated with two of the measured frequencies (F1 and F2) will be markedly higher than the voltage amplitude associated with the other two and the latter may not exhibit excursions below the zero phase reference.
Since such zero crossings are necessary for accurate frequency measurements, U.S. Pat. No. 5,049,828 to Toliver et al. discloses a compensation circuit to establish these zero phase reference points in the Peppiatt and Roberts transmission measurement system when applied to high frequency and/or high resonator resistance crystals. However, there are several problems with the compensation approach disclosed in the Toliver patent. It adds at least two additional circuit elements to the original fixture shown in FIG. 4 of U.S. Pat. No. 5,049,828 and it must be set or tuned to produce the required zero phase crossings. It is usually tuned to produce the four frequencies at the final crystal test operation. It, therefore, tends to have accuracy problems at frequencies other than final frequency. Separate fixtures must be used for coupled-dual resonator crystals in different frequency ranges. There also tend to be correlation problems from fixture to fixture whenever a fixture must be set by a variable coil/capacitor combination.
Therefore, the need arises as to how to determine the values of the four critical frequencies, F1, F2, F3 and F4, for the cases taught in U.S. Pat. Nos. 4,093,914, 5,047,726 and 5,049,828 for those situations where the phase responses do not provide undiminished zero phase crossings without external compensation.
Another parameter calculated from the four critical frequencies and extremely important in developing or evaluating a coupled-dual resonator monolithic crystal filter is the inductance of each resonator. Accurate determination of inductance enables the proper coupling of two or more coupled-dual crystals together to form a filter and allows for the correct termination of the filter. Prior to the present invention, resonator inductances were assumed to be the values determined from measuring each resonator's electrode dimensions after an electrode pattern had been plated onto the crystal wafer at the baseplate operation. However, the actual inductance of each resonator could not be measured with this method accurately. In the early 1970s, it was discovered that a coupled-dual crystal resonator measured around either one of two transmission peak resonances produced approximately twice the inductance of one of the two resonators or approximately the sum of the two resonator inductances, as most coupled-dual resonator crystal designs produced resonators with equal inductances. However, this scheme only provided an approximate value of the inductances of a coupled-dual resonator crystal and often contained substantial errors. The inductance measurement inaccuracies were noticed to increase significantly at higher frequencies (i.e., at 30 megahertz and above). In addition, this process required substantial hardware and software.
Therefore, what is needed is a method for accurately determining resonator inductances of a coupled-dual resonator crystal at both low and high frequencies.